Problem: Multiply the following complex numbers, marked as blue dots on the graph: $[5(\cos(\frac{1}{4}\pi) + i \sin(\frac{1}{4}\pi))] \cdot [2(\cos(\pi) + i \sin(\pi))]$ (Your current answer will be plotted in orange.)
Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $5(\cos(\frac{1}{4}\pi) + i \sin(\frac{1}{4}\pi))$ ) has angle $\frac{1}{4}\pi$ and radius $5$ The second number ( $2(\cos(\pi) + i \sin(\pi))$ ) has angle $\pi$ and radius $2$ The radius of the result will be $5 \cdot 2$ , which is $10$ The angle of the result is $\frac{1}{4}\pi + \pi = \frac{5}{4}\pi$ The radius of the result is $10$ and the angle of the result is $\frac{5}{4}\pi$.